Electric Circuits Answers

Two helical coils of the same length but with different radii are arranged such that one is placed inside the other and both are co-aligned along the same central axis running along their length. They share a mutual inductance which can vary as a function of time by sliding the inner coil out of the outer coil. Calculate the EMF induced in the outer coil at the instant when

i. A current changes through the inner coil at a rate of 5 A s−1 and the mutual inductance is 0.4 mH.

ii. The current through the inner coil is 2 A and changing at a rate of 5 A s−1 and the mutual inductance is 0.4 mH but changing at a rate of 30 mH s−1.

iii. The current through the inner coil is fixed at 2 A and the mutual inductance is changing at a rate of 30 mH s−1.

You are tasked with manufacturing Christmas tree lights for a company that you work for. You will need to be produce a good quality, but cost effective, product. Thinking about series and parallel circuits, how will you set the lights up and why?

1. Using the definition C=Q/V, show that for a SERIES connection of capacitors: 1/C = 1/C1 + 1/C2. What does this equation mean? What happens to C as more and more capacitors are connected in series?
2. Using the definition C=Q/V, show that for a PARALLEL connection of capacitors: C= C1+C2. What does this equation mean? What happens to C as more and more capacitors are connected in parallel?

A coil of wire is made of 520 turns and has an area of 0.30 m^2. It is placed in a uniform magnetic field of magnitude 0.40 T. This magnetic field flips its orientation from 0.40 T in the +y-direction to 0.40 T in the −y-direction in 2.0 s. How much power is generated in the coil if it has a resistance of 1200 Ω ?

 A 35 𝜇𝐶 point charge is placed 32 𝑐𝑚 from an identical 32 𝜇𝐶 charge. How much work would be required to move a 0.50 𝜇𝐶 charge from a point midway between them to a point 12 𝑐𝑚 closer to either of the charges?

What is the temperature coefficient of resistance of a piece of wire having a resistance of 11.56 ohms at 25°C and 10.22 ohms at 0°C? What will be its resistance at 50°C?

A 2.0 cm x 3.0 cm rectangle lies in the xy-plane. What is the electric flux through the rectangle if;

𝐸
⃗ 
= (100 
?̂
+ 50 
𝑘
̂
) N/C

A water heater has a resistance of 5.3 ohms and takes 43.5 amp when in operation. If itis in service on the average of 2 hr per day, how many kilowatt hours of energy will be expended during a 30 day month?"

A square current loop is placed in a uniform magnetic field of magnitude 0.65 T directed into the page. The loop’s side length changes from 20.0 cm to 6.0 cm in 0.50 s.

(a) What is the magnitude of the induced emf?

(b) If the loop has a resistance of 2.5 Ω, then what is the magnitude of the induced current?

A coil of wire contains three loops. If the magnetic flux through the coil changes from −45 Wb to +52 Wb in 0.36 s, what is the magnitude of the emf induced in the coil